Modelling and Forecasting Noisy Realized Volatility

Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility errorâ€. Since such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper.forecasting;diffusion;financial econometrics;goodness-of-fit;measurement errors;model evaluation;realized volatility

Log Skeletons: A Classification Approach to Process Discovery

To test the effectiveness of process discovery algorithms, a Process Discovery Contest (PDC) has been set up. This PDC uses a classification approach to measure this effectiveness: The better the discovered model can classify whether or not a new trace conforms to the event log, the better the discovery algorithm is supposed to be. Unfortunately, even the state-of-the-art fully-automated discovery algorithms score poorly on this classification. Even the best of these algorithms, the Inductive Miner, scored only 147 correct classified traces out of 200 traces on the PDC of 2017. This paper introduces the rule-based log skeleton model, which is closely related to the Declare constraint model, together with a way to classify traces using this model. This classification using log skeletons is shown to score better on the PDC of 2017 than state-of-the-art discovery algorithms: 194 out of 200. As a result, one can argue that the fully-automated algorithm to construct (or: discover) a log skeleton from an event log outperforms existing state-of-the-art fully-automated discovery algorithms.Comment: 16 pages with 9 figures, followed by an appendix of 14 pages with 17 figure

Asymmetry and leverage in realized volatility

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In both the conditional and stochastic volatility literature, there has been some confusion between the definitions of asymmetry and leverage. In this paper, we first show the relationship among conditional, stochastic, integrated and realized volatilities. Then we develop a new asymmetric volatility model, which takes account of small and large, and positive and negative, shocks. Using the new specification, we examine alternative volatility models that have recently been developed and estimated in order to understand the differences and similarities in the definitions of asymmetry and leverage. We extend the new specification to realized volatility by taking account of measurement errors. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index using Efficient Importance Sampling to show the new specification of asymmetry significantly improves the goodness of fit.

Dark matter spikes in the vicinity of Kerr black holes

The growth of a massive black hole will steepen the cold dark matter density at the center of a galaxy into a dense spike, enhancing the prospects for indirect detection. We study the impact of black hole spin on the density profile using the exact Kerr geometry of the black whole in a fully relativistic adiabatic growth framework. We find that, despite the transfer of angular momentum from the hole to the halo, rotation increases significantly the dark matter density close to the black hole. The gravitational effects are still dominated by the black hole within its influence radius, but the larger dark matter annihilation fluxes might be relevant for indirect detection estimates.Comment: Published version plus corrected typo in Fig 1

Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin

Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time

Starting from a recently proposed Abelian topological model in (2+1) dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for generalization is detected. However we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore in order to quantize the theory we construct a complete set of BRST and anti-BRST equations using the horizontality condition.Comment: 8 pages. To appear in Physical Review

Non-Chern-Simons Topological Mass Generation in (2+1) Dimensions

By dimensional reduction of a massive BF theory, a new topological field theory is constructed in (2+1) dimensions. Two different topological terms, one involving a scalar and a Kalb-Ramond fields and another one equivalent to the four-dimensional BF term, are present. We constructed two actions with these topological terms and show that a topological mass generation mechanism can be implemented. Using the non-Chern-Simons topological term, an action is proposed leading to a classical duality relation between Klein-Gordon and Maxwell actions. We also have shown that an action in (2+1) dimensions with the Kalb-Ramond field is related by Buscher's duality transformation to a massive gauge-invariant Stuckelberg-type theory.Comment: 8 pages, no figures, RevTE